Anyone has seen anything like this or has anyway to troubleshoot this?
Lots of, in most cases it's a software failure, often caused by a RAM overflow. Show us your code. I guess it's not Webduino getting unstable but any part of the rest of the sketch.
BTW, if you use the wallwart to power the board, I cannot use the serial USB to debug the program - it will actually get the equivalent of the blue screen of death on my Mac (which I did not even ono existed). So how do you debug besides lots of recompiles and blinking a LED or something like that...
I never experienced something like that but I don't have a Mac. If your computer crashes it has nothing to do with your Arduino but only with your operating system or probably with the driver for the USB2Serial chip (FTDI). Do you have another USB2Serial which uses another driver (Arduino USB2Serial Light as an example)?
If you don't use the wallwart for powering the board, you don't experience crashes on your Mac? If powered by the wallwart, have you connected the 5V line of the FTDI cable to the Arduino? Try connecting just the other 4 pins (GND, RST, TX, RX).